WIPING perspiration from his brow, Nigel Farage headed to the Reform Club in London’s Pall Mall to raise a glass or three in celebration of his live broadcast debate triumph over Nick Clegg.

BATTLE: Ukip’s Nigel Farage (left) was seen as the winner in the debate with Nick Clegg (right)[GETTY]

The Ukip leader could hardly have chosen a more appropriate venue; the palatial club house was once the HQ of the old Liberal Party and is adorned with portraits of Liberal leaders of the past. William Gladstone, Herbert Asquith, David Lloyd George; your boys took one hell of a beating.

Or so Mr Farage could have been forgiven for thinking. Friends say the Tiggerish politician was even more chipper than usual at the gathering for a select group of Ukip supporters and donors. He had good reason to celebrate.

Opinion polls have declared the leader of the anti-Brussels party the undisputed victor in Wednesday night’s historic live leaders’ debate on Britain’s future in Europe. The popular verdict confounded the expectations of many, dispelling their hopes that the Ukip phenomenon is past its sell-by-date.

After a couple of years of spectacular poll advances, the party has been through a difficult few months. Opponents in the established parties were questioning whether it had reached the limit of its appeal. Sweaty and a little unpolished he may have been, yet Mr Farage proved himself to be a serious contender who articulates the concerns of voters fed up with the three main Westminster parties.

Mr Clegg will have to work harder over the next few days to be better prepared for another onslaught from the Farage bulldozer in this Wednesday’s rematch on BBC2. But aides insist the Lib Dem leader, who issued the debate challenge in the first place, is not too downhearted.

Mr Clegg never envisaged that his enthusiasm for the European Union was going to win over the majority of the audience. His high-risk gamble in taking on Mr Farage was always intended to shore up the Lib Dem core vote. The aim is to stop the Lib Dems suffering a catastrophic meltdown in May’s Euro elections that could leave his party without a single Euro MP.

To that purpose, Mr Clegg will have been heartened that his biggest cheer of the night from the studio audience came in reaction to his passionate celebration of the coalition’s decision to legalise same-sex weddings.

Ukip and the Lib Dems are courting very different groups of voters in their tussle over the third-place spot in the party system. The real question for Westminster is how David Cameron and Ed Miliband respond. Labour sources say the party’s private polling shows that Ukip voters are primarily a problem for the Conservatives and dismiss claims that the anti-Brussels party is making inroads in their traditional working-class heartlands.

In contrast, the Tories appear braced for a drubbing at the Euro elections and are hoping to regain ground from Ukip in the run up to next year’s general election. “The fact is that voters see the European elections as an opportunity to protest. We can argue that maximising the number of Conservative Euro MPs in the European Parliament will help David Cameron in his negotiations for a new EU deal for Britain, but that is not going to be a hugely strong argument with people who are angry about immigration,” one senior Tory admitted.

As May 2015 approaches, the Tories will continually emphasise their case that only returning Mr Cameron to 10 Downing Street can deliver an in-or-out referendum on Britain’s membership. That may be a persuasive case for some passionate Euro sceptics. But the applause for Mr Farage in the debate, particularly on the issue of immigration, confirms his appeal to a wider set of voters who are disenchanted with the political establishment.

His conviction that Britain’s borders cannot be controlled as long as Britain remains bound to the EU’s freedom-of-movement rules is difficult to dispute. Tory ministers will struggle to counter that charge unless they can make more progress in reaching Mr Cameron’s target of reducing annual net immigration to the “tens of thousands”.

The Tories need to set out an inspiring vision of what the country could look like under a Conservative-only government to give voters a positive reason to back them. There are signs that is happening, with the revival of the Tory pledge to cut inheritance tax, the overhaul of pensions and reductions in income tax and levies on beer and Bingo.

A strong narrative about giving people control of their own money and setting them free to spend it as they choose is developing at last.

Mr Cameron has made a start in facing up to the Ukip challenge. But this week’s Europe debate confirms that it is the Prime Minister, just as much as Mr Clegg, who is facing the mother of all battles with Mr Farage.